Technical Mathematics Grade 12 Paper 2 NSC November 2019 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 12/GRAAD 12 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 NOVEMBER 2019 FINAL/FINALE MARKING GUIDELINE/NASIENRIGLYN MARKS/ PUNTE: 150 CODE/KODE EXPLANATION/VERDUIDELIKING A Accuracy/Akkuraatheid AO Answer Only/Slegs antwoord CA Consistent accuracy/Konsekwente akkuraatheid I Identity/Identiteit F Correct Formula/Korrekte formule M Method/Metode NPR No penalty for rounding/Geen penalisering vir afronding NPU No penalty for units/Geen penalisering vir eenhede R Rounding/Afronding RE Reason/Rede S Simplification/Vereenvoudiging SF Substitution in correct Formula /Vervanging in korrek Formule ST Statement/Bewering ST/RE Statement with Reason /Bewering met rede These marking guidelines consists of 29 pages. Hierdie nasienriglyne bestaan uit 29 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 2 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne NOTE:  If a candidate answers a question TWICE, only mark the FIRST attempt.  Consistent accuracy to be applied as indicated on the marking guidelines.  # Questions where Tolerance Range will be applied are Q4.2.2, Q6.3, Q10.1.3 and Q11.2.3. LET WEL:  Indien 'n kandidaat 'n vraag TWEE keer beantwoord, sien slegs die EERSTE poging na.  Volgehoue akkuraatheid sal toegepas word soos op die nasienriglyne van aangedui.  # Vrae waar Toleransie Wydte toegepas word is V4.2.2, V6.3, V10.1.3 en V11.2.3. QUESTION/VRAAG 1 1.1  L1 OED  76     104   angle/hoek A AO: Full marks/Volpunte (1) 1.2 AF   2  (8)2  8  (4)2  SF A L2  36  144  180  length in simplified surd form/ 6 5 lengte in vereenvoudigde wortelvorm CA AO: Full marks/Volpunte (2) 1.3 m  tan  L2  tan 76   SF A 4  gradient/gradiënt (rounded/afgerond) AO: Full marks/Volpunte (2) 1.4   2  (8) 8  (4)   SF A L1 M AF  ;   2 2   S coordinates of/koördinate van M AF A M AF  5 ; 2 AO: Full marks/Volpunte (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 3 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 1.5 y2  y1 L2 mAF  x2  x1 8  (4) 82  42  OR/OF  OR/OF   SF A  2  ( 8)  2  ( 5)  8  (  5)  2  gradient of/gradiënt van mAF 1  mperpend   CA 2  gradient of/gradiënt van mperpend CA y  2 1 x  (  5 ) OR/OF 2  1  5  c  SF CA from Q 1.4 2 2 1 5 1 y x 2 OR/OF c   2 2 2 1 1  equation/vergelyking CA y  x  2 2 (5) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 4 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1.1 x 2  y 2  (  4 )2  (  3 )2  SF A L1 OR/OF x 2  y 2  ( 4 )2  (  3 )2  equation/vergelyking A  x  y  25 2 2 OR/OF y   25  x 2 AO: Full marks/Volpunte (2) 2.1.2(a) B( 4 ; 3)  coordinates of/ L1 koördinate van B A (1) 2.1.2(b) 4  gradient of/gradiënt van L1 mPQ   PQ A 3 (1) 2.1.3 4  SF CA L2 y  3   ( x  4) 3 from/van 4 16 Q/ V 2.1.2(a) & (b) y   x  3 3 3 S CA 4 25 y   x  equation/vergelyking 3 3 CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 5 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne y  mx  c  SF CA 3   4   c 4 3 from/van Q/V 2.1.2(a) 25 & (b) c 3  value of/waarde van c 4 25 CA y   x  equation/vergelyking 3 3 CA (3) 2.2.1 x 2  8 y 2  32  0 L1 1 2 8 2 32 dividing both sides/deel x  y  albei sye by/deur 32 32 32 32 and/en transposing/oordra A x2 y2  1 correct surd form/ 4 2  2 22 korrekte wortelvorm CA Accept: AO: Full marks/Volpunte (2) 2.2.2 L2 CA from/van Q/V 2.2.1 both y-intercepts/ beide y-afsnitte CA  both x-intercepts/ beide x-afsnitte CA  elliptical shape elliptiese vorm CA (3) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 6 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 sin 3  sin 3(32) L1  0,99  value of /waarde van sin 3 A NPR (1) 3.1.2 sec   1 sec 20  1 2 2 L1  tan  tan 32 2  1   1   I   A   1  cos 20    cos 20   tan 32  value of/waarde van  0, 21 sec 2   1 CA tan  OR/OF OR/OF sec 2   1 tan 2 20 I A  tan  tan 32  0, 21  value of/waarde van sec 2   1 CA tan  NPR AO: Full marks/Volpunte (2) 3.2.1 L2 x r m2  1 r A 1  definition of/ sin 35  m2  1 definisie van sin CA AO: Full marks/Volpunte (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 7 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 3.2.2  29   7   cos    tan    36   36   cos145 tan 35  changing to degrees/  sin 35  verander na grade A    cos 35    cos 35 CA  cos 35   I A   sin 35 S CA 1    ratio/verhouding CA m2  1 OR/OF OR/OF  29   7   cos    tan    36   36   cos145 tan 35  changing to degrees/   cos 35 tan 35 verander na grade A   cos 35 CA   1      m  m  1   m  2  ratio of/verhouding van  cos CA   1  ratio of/verhouding van m2  1 tan A S CA OR/OF OR/OF  29   7   cos    tan    36   36    29   7    cos       tan    reduction/reduksie   36   36  A  7   sin    7  7    cos    36    cos  CA  36   7  36  cos    36  I A 7   sin    sin 35 S CA 36 1   m2  1  ratio of/verhouding van sine CA (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 8 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 3.3.1 2 cos   sin   0 L2 sin    2 cos   transposing/oordra A sin   2 cos   ; cos   0 cos  cos   M dividing both sides  tan    2 by/deel beide kante deur cos  A (2) OR/OF OR/OF 2 cos    sin   transposing/oordra A 2 cos  sin   ; sin   0  M dividing both sides sin  sin  by/deel beide kante 1 deur sin  A cot    2 1 1  tan  2 tan  2 (2) 3.3.2 tan   2 L2 Ref/verw.   63, 43  ref/verw A nd th de de   180  63, 43 or/of   360  63, 43  2 & 4 /2 en 4 quadrants/kwadrante A   116 , 57 or/of   296 , 57  116 , 57 CA  296 , 57 CA AO: Full marks/Volpunte (4) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 9 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1.1 cot 2 2  cosec 2 2   1 –1 A L1 (1) 4.1.2 tan 2 A  cosec 2 A  cos2π L3 sin 2 A 1  sin A    2 1 I   A 2 cos A sin A  cosA  1 I A  1 cos 2 A 1 A 1  cos 2 A sin 2 A   I CA cos 2 A cos 2 A  tan 2 A S CA OR/OF OR/OF tan 2 A  cosec 2 A  cos2π sin 2 A 1  2  2 1  sin A  cos A sin A I   A  cosA  1 I A  1 1 A cos 2 A  sec 2 A  1 I CA  tan 2 A S CA OR/OF OR/OF tan 2 A  cosec 2 A  cos 2  tan 2 A (1  cot 2 A)  1 I A 1 A  tan 2 A  tan 2 A  cot 2 A  1  product/produk CA  tan A  1  1 2 1 CA  tan 2 A S CA (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 10 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 4.2.1 sec 60  2 2 A L1 (1) 4.2.2 cosec (180   )  sin (360   )  sin(180   ) sec 60  cos 2  L4 # L.H.S/LK  cosec (180   ) sin (360   )  sin(180   ) 2   cosec    sin    sin 2 (180   )   cosec  A  1    sin  A       sin     sin   2  I  sin   A   sin  A  1  sin 2   cos 2   R.H.S./RK  S 1  sin 2  CA (5) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 11 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 360  period/periode A L1 (1) 5.2 a2  value of/waarde van a A L1 b 2  value of/waarde van b A (2) 5.3 T (158 , 5 ;  0 , 7 )  x coordinate/koördinaat A L1  y coordinate/koördinaat A Accept: T (159 , 5 ;  0 , 7 ) (2) 5.4.1 135  x  180  end points/eindpunte A L2 OR/OF  correct notation/korrekte notasie A x 135 ;180 (2) 5.4.2 x  45 or/of x  135  x  45 A L1  x  135 A (2) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 12 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 150  trig ratio/verhouding A L cos 50  AC 150  the subject/ AC  die onderwerp AC CA cos 50  233 , 36 m  length of/lengte van AC CA OR/OF OR/OF AB  150 tan 50  Length of AB A M CA AC  (150tan50) 2  (150) 2  length of/lengte van AC  233 , 36 m CA OR/OF OR/OF  BAC  40 sin 40  150  trig ratio/verhouding A AC 150  the subject/ AC  OR/OF = 150 cosec40 die onderwerp AC CA sin 40  233,36 m  length of/lengte van AC CA OR/OF OR/OF  BAC  40 150  AC  SF A sin 40 sin 90  the subject/ 150 sin 90 die onderwerp AC CA AC  sin 40  length of/lengte van AC  233 , 36 m CA NPR (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 13 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 6.2 1 F A L3 Area of/oppervlakte van ACD   AC  CD sin  2 1 3,3648 104   233,36  300  sin   SF CA 2 from/van Q/V 6.1 3,3648 104 2804 S CA sin     0,96126157 35004 2917  ref . / verw.∠ CA ref / verw.   74   180  74  size of/grootte van    106 CA OR/OF OR/OF 1 Area of/oppervlakte van ACD   AC  CD sin  F A 2 1 3,3648 104   233,36  300  sin  2  SF CA 3,3648 10  35 004sin  4 from/van Q/V 6.1 S CA 3,3648 104 sin   35004 ref / verw.   74  ref . / verw.∠ CA   180  74  size of/grootte van    106 CA NPR (5) 6.3  L2 AD2  AC2  DC2  2AC  DC cos ACD F A  ( 233 , 36 ) 2  ( 300 ) 2  2 ( 233 , 36 ) ( 300 ) cos 106  SF CA #  183 050 , 5296 from/van Q/V 6.1, 6.2 S CA AD  427 , 84 m  length of /lengte van AD CA NPR (4) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 14 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1 Perpendicular to the chord/loodreg op die koord  ST A L1 (1)   ST A L1 7.2.1(a) C1  26, 6ο [ s in thesame segment (arc or chord)/  RE A ein dieselfde segment (boog of koord )] OR/OF OR/OF  4  ratio/verhouding A sin C1  4 5    size of/ grootte van C1  C1  26,6 ο A (2)  L1 7.2.1(b) A  180 ο  90 ο  26,6 ο [ sum/som s ]  ST CA  63,4ο from/van Q/V 7.2.1(a) OR/OF OR/OF  ext.  of   sum of 2 int. opp. s  90  A  26, 6    ST CA buite  van   som teenrst binne e  from/van Q/V 7.2.1(a)  A  63,4 ο OR/OF OR/OF 4 5 cos A   4 5 5  5  A  cos 1    63 , 4   ST A  5  (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 15 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne  L1 7.2.1(c) B1  90ο  26,6 [  in semi circle/in halfsirkel ]  ST A  63,4ο  RE A OR/OF OR/OF  4 cos B1   cos ratio/ verhouding 4 5  A B1  63 , 4  ST A OR/OF OR/OF   s opp. equal sides/e teenoor gelyke sye /  ST A A  B1  63, 4   RE A  OE  AB and/ en AE  EB  (2) 7.2.2(a) AE  4 units/eenhede  length of /lengte van L1 AE A (1) 7.2.2(b) ED  5  x units/eenhede  length of /lengte van L1 ED A (1) 7.2.3 42  x  5  4 5 2   2 M A L3 16  x 2  10 x  25  80 x 2  10 x  39  0 S CA x  3x  13  0  factors/ formula x  3 or/of x   13 faktore/ formule CA  correct value of / korrekte waarde van x One mark penalty if a candidate include as the CA answer/ Een punt penalisering indien die kandidaat as antwoord insluit OR/OF OR/OF 5 x  tan ratio/verhouding A  tan 26 , 6 S CA 4 5  x  4 tan 26 ,6 S CA  correct value of / 5  x  2,003  2 korrekte waarde van x x  2,997  3 CA OR/OF OR/OF x  (5)  (4) 2 2 2  Th. of Pythagoras A  subst./verv. CA x2  9 S CA x 3  correct value of / korrekte waarde van x CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 16 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 4h 2  4dh  x 2  0 4h 2  4(10)h  (8) 2  0  SF A 4h  40h  64  0 2 h 2  10h  16  0 ( h  8) ( h  2 )  0  factors/ formula h  8 or h  2 faktore/ formule CA  both values of/ beide EC  x  5 waardes van h CA 8x5 x 3  correct value of / korrekte waarde van x CA OR/OF OR/OF x5 sin 63 , 4   sin ratio/ verh A 4 5  substitution/ 8x5 vervanging A x 3 S CA  correct value of / korrekte waarde van x CA OR/OF OR/OF    4 CE 2  4 5 2 2  Theorem of Pyth.  substitution/ A CE 2  64 vervanging A CE  8  value of/ waarde van x85 CE CA x  3  correct value of / korrekte waarde van x CA AO: Full marks/Volpunte (4) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 17 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1 90 / Right angle/ Regte hoek  90 / Right angle/ Regte hoek L1 A (1) L1 8.2.1(a)   ST A CBO  90ο  30ο [tan  radius (diameter)/  RE A raaklyn  radius (middellyn )] (2)  60ο  L1 8.2.1(b) D 2  30 ο [tan  chord/raaklyn  koord]  ST A  RE A (2)  L2 8.2.1(c) O1  60ο [ at centre  2  at circumfere nce/  ST CA middlepunt   2 omtreks] from/van Q/V 8.2.1 (a)  RE A OR/ OF OR/ OF ^ O BA  90  rad  tan/raaklyn ^  O B C  60 ^   O B C  C3  60  ST CA from/van Q/V 8.2.1 (a)  s opp. equal sides, OC and OB radii /  e teenoor gelyke sye, OC en OB radii     sum of s of  /   ST A O1  180  120  60   (2)  som van e van Δ Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 18 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne L2 8.2.1(d) ∧ ∧ corresp∠s / ooreenk ∠e  ST A O1  E  60ο    CO || FE    D4  E  60ο  s opp.  sides/e teenoor  sye ]  ST A   O2  D4  60 ο [ Alt s /verw.e, CO || FE]  ST A (3) ∧ ∧ ext ∠ of cyclic quad/  ST CA L4 8.2.2 C1  E  60 ο buite ∠van koorde vierh. RE A   ∧ ∧ ext ∠ of cyclic quad/  D1  CBO  60ο   ST CA buite ∠van koorde vierh. sides opposite s /   FC  FD    RE  sye teenoor  e A  OR/OF OR/OF FB  FE  sides opp.   s / sye teenoor  e  ST CA DE  CB equilateral /gelyksydige  RE A  ST CA FB  CB  FE  DE M A  FC  FD (4) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 19 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1 Parallel to the third side/Ewewydig aan die derde sy  ST A L1 (1)  L2 9.2.1 OGC  90  tan  radius/raaklyn  radius  ST A  RE A OEF  90  [ OG  GC ]  DF || BC [corr. s are equal/ ooreenk . e is gelyk ]  RE A (3) 9.2.2  proportionality/eweredigh L2 (a) BC : DF  10 : 6  5 : 3 A  simplified ratio/ vereenv.verhouding A OR/OF OR/OF  ODF ///  OBC OD OF DF 3  proportionality/eweredigh    A OB OC BC 5  simplified ratio/  BC : DF  5 : 3 OR/OF BC : DF  10 : 6 vereenv.verhouding A AO: Full marks/Volpunte (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 20 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 9.2.2 EG 2 proportionality/eweredigh A L2 (b)  OG 5 EG 2  substitution/vervanging A 6 5 12 EG  units / eenhede OR / OF 2, 4 units /eenhede length of /lengte van EG CA 5 OR/OF OR/OF OD OE  proportionality/eweredigh  OB OG A 3 OE  5 6  substitution/vervanging A 18 OE   3, 6 5  length of /lengte van EG EG  6  3 , 6  2 , 4 CA (3) 9.2.2 L3 (c) OE  6  2 , 4  3, 6 units/eenhede  length of /lengte van OE 1  CA Area (Opp.)  OBG  10  6  sin BOG from /van Q/V 9.2.2 (b)  2   SF CA Area (Opp.)  ODE 1  6  3, 6  sin BOG 2  value/waarde CA 25  9 OR/OF OR/OF 1 Area (Opp.)  OBG  BG  OG   2 Area (Opp.)  ODE 1  DE  OE  2  length of /lengte van OE 5 6   CA from/van Q/V 9.2.2 (b) 3 3, 6  SF CA 25  value/waarde CA  9 OR/OF OR/OF 1 Area (Opp.)  OBG  4,8 3, 6   length of /lengte van DE  2 Area (Opp.)  ODE 1 CA from/van Q/V 9.2.2 (b) 8 6   SF CA 2 24  8, 64  2, 78  value/waarde CA (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 21 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 9.3 In  DOE and/en  BOG L4   DOE  BOG common /gemene  ST A   OED  OGB  90  proved / bewys   ST A    ODE  OBG 3rd/3de   RE A   DOE |||  BOG  OR/OF OR/OF In  DOE and/en  BOG OE 3 , 6 3  one ratio/verh A   OG 6 5  two ratios/verh A OD 6 3   OB 10 5 DE 3  BG 5 corr.sides are in proportion/   RE A   DOE |||  BOG ooreen. sye is eweredig    (3) [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 22 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 10 /Band /Velling 10.1.1 BC = 20 cm – 1,5 cm L1 = 18,5 cm  length of /lengte van BC A (1) 10.1.2 4h 2  4dh  x 2  0 F A L3 4h 2  4(40)h  (32) 2  0  SF A 4h  160h  1024  0 2 4(h 2  40h  256)  0 4(h  32)(h  8)  0  factors/formula/faktore/formule h  32 or / of h  8 CA h  AC  8 cm  length of /lengte van AC CA  AB  18,5 cm  8 cm  10,5 cm  length of /lengte van AB CA OR/OF OR/OF OC  1  40   20 cm  length of /lengte van OC A 2 OC  OK  20 cm radii OK  KA  OA 2 2 2  SF A ( 20 ) 2  (16 ) 2  OA 2  length of /lengte van OA CA OA  12 cm AB  12  1, 5 cm  10 , 5 cm  AB  12  1, 5 CA  length of /lengte van AB CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 23 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne In  OAL : OC  OL  20 cm radii  length of/ lengte van OL A OL2  OA 2  AL2 (20) 2  OA 2  (16) 2  substitution/ vervanging A 400  256  OA 2 OA  144  12  value of / waarde van OA CA AB  OA  OB  12  1, 5 M CA  10 ,5 cm  length of /lengte van AB CA (5) 10.1.3 w  64 rad/min L2  64  2 rad/min  128 2 rad/min  conversion A OR/OF 1263,13rad/min   2 n 128 2  2 n OR/OF 1263,13  2 n  SF CA 128 2 2 n  2 2  n  64  rev/min OR/OF  201, 03 rev/min  value of /waarde van n CA (3) 10.1.4 v   Dn F A L2    40 cm    64    SF CA  v  25266,19 cm/min  value of v CA OR/OF  unit CA  v  421,10 cm/sec OR/OF  v  4, 21 m/sec OR/OF  v  252, 66 m/min Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 24 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne OR/OF OR/OF v   Dn    40 cm    64   F A  v  25266,19 cm/min  SF A OR/OF  value of / waarde van v CA  v  421,10 cm/sec  unit/ eenheid CA OR/OF  v  4, 21 m/sec OR/OF  v  252, 66 m/min (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 25 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 10.2 4 M A L2 10.2.1 A O B  4  20  80    magnitude of/grootte 9   1, 4 van A O B A   in radians/ in radiale CA OR/OF OR/OF ∧ 4 4 AOB   360  80   M A 18 9  magnitude of/grootte  1, 4  van A O B A   in radians/ in radiale CA OR/OF OR/OF P  2r  2 (5 , 2)  32 , 67.....cm  Perimeter/ omtrek A 32, 67 Dist. between each spoke/ Afst. tussen elke speek  1,815...cm 18 AB  4  1,815.....  7 , 26....cm s  r 7 , 26....  (5 , 2)  SF A   1, 4   in radians/ in radiale CA (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 26 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne s  r F A L2 10.2.2 4  5 , 2 cm  1, 4 or / of 5 , 2 cm    SF CA 9  arc length/booglengte  7 , 3 cm CA OR/OF OR/OF 4 M A s  2r 18 4 4   2 ( 5, 2 ) cm  A 18 18  7, 3 cm  arc length/ booglengte CA (3) 10.2.3 rs L2 Area of a sector/opp. van sektor  2 F A 5, 2  7 , 3   SF CA 2  19 cm 2  area of sector/Opp.van sektor CA OR/OF OR/OF r 2s F A Area of a sector/opp. van sektor  2  SF CA  5 , 2 2  1, 4 2  area of sector/Opp.van  19 cm 2 sektor CA OR/OF OR/OF 4 Area of a sector/Opp.van sektor   r2  ratio/verh A 18    5, 2  cm 2 4 2  substitution/ vervang 18 CA  19 cm 2  area of sector/opp van sektor CA (3) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 27 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 11 11.1.1 b 2 L1  value of /value of b A  1,4 m NPR (1) 11.1.2 2  value of /waarde van L3 A Irr  19,125 m 2  12, 75 m 2 3 A Irr A A T  a  m1  m2  m3  ...  mn  F A  value of /waarde van  1,8  2 2  1, 4 1, 4  1,3 1,3  1,8 1,8  q  12, 75 1,5       a A  2 2 2 2 2   SF CA  1,8  q  12, 75 1,5 1,9  1, 7  1,35  1,55    2  1,8  q 8,5  6,5  2 4  1,8  q  value of /waarde van q CA  q  2, 2 m OR/OF OR/OF 2 A Irr   19,125 m 2  12, 75 m 2  value of/waarde van 3 A Irr A  1,8  q  12, 75 1,5   2  1, 4  1,3  1,8  F A  2  1,8  q  value of /waarde van 8,5  6,5  2 a A 4  1,8  q  SF CA  q  2, 2 m  value of /waarde van q CA (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 28 DBE/November 2019 NSC/NSS – Marking Guidelines/Nasienriglyne 11.2 11.2.1 V lbh L1 70 m  3 , 5 m  10 m  h 3  h  2m  value of h A (1) 11.2.2 1 L1 r   3 , 5 m  1, 75 m  value of r A 2 (1) 11.2.3 SA Rec.Prism  2   b  h   2   l  h  L4  SF CA from Q11.2.1  2   3,5 m  2 m   2  10 m  2 m  #  value of / waarde van  54 m 2 A Prism CA SA 1 cylinder 1    2 r 2  2 rh 2  2 1   2 (1, 75) 2  2 (1, 75)(10)  m 2  SF CA from Q11.2.2 2  20,56  m 2 OR/OF  64, 60 m 2  value of /waarde van A2 1 CA SA T  54 m 2  64, 60 m 2 OR/OF  54 m 2  20,56  m 2 silinder  118, 60 m 2  SA total/totaal CA YES, the total surface area is less than 120 m 2  conclusion must be JA, die totale buite-oppervlakte is minder as 120 m2 based on total surface area/gevolgtrekking moet gebaseer word volgens die totale buite-oppervlakte CA (6) [14] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou